You have a tank of helium with a volume of 10 liters that is currently under 40 atm of pressure. If you open the valve on the tank and release the helium into a room with a volume of 10,000 liters, how many atmospheres of pressure will the helium now be under? Second, what will happen to the "space" between the helium atoms? Clearly explain your answer, including any assumptions you may need to make in order to answer the question

Steve answered your question.

To answer the first part of your question, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is constant.

Let's calculate the new pressure of the helium in the room using Boyle's Law. We have the initial pressure (P1) as 40 atm and the initial volume (V1) as 10 liters. The final volume (V2) is given as 10,000 liters. Since the temperature is not given, we will assume it remains constant.

According to Boyle's Law, P1 * V1 = P2 * V2, where P2 is the final pressure.

Substituting the given values, we have:
40 atm * 10 liters = P2 * 10,000 liters

Simplifying the equation, we get:
400 atm * liters = P2 * 10,000 liters

Dividing both sides by 10,000 liters, we find:
40 atm = P2

Therefore, the helium will now be under 40 atmospheres of pressure in the room.

Now, let's move on to the second part of your question. When the valve is opened and the helium is released into the room, the space between the helium atoms will essentially expand. This is because the volume of the room is much larger than the volume of the tank.

In the tank, the helium molecules are confined to a smaller volume, resulting in more frequent collisions with each other and the walls of the tank. When released into the room, the helium molecules will have more space to move around, reducing the frequency of collisions. This expansion of the gas will cause the space between the helium atoms to increase, though the individual helium atoms themselves will not change in size.

It is worth noting that we are assuming an ideal gas behavior for helium in our explanation. In reality, helium does deviate slightly from ideal behavior at very high pressures and low temperatures, but for the purpose of this explanation, we can assume ideal gas behavior.